There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ acrsin(\frac{x}{2}) - xcos(acrsin(\frac{x}{2})) - sqrt(3)x\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = acrsin(\frac{1}{2}x) - xcos(acrsin(\frac{1}{2}x)) - xsqrt(3)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( acrsin(\frac{1}{2}x) - xcos(acrsin(\frac{1}{2}x)) - xsqrt(3)\right)}{dx}\\=&acrcos(\frac{1}{2}x)*\frac{1}{2} - cos(acrsin(\frac{1}{2}x)) - x*-sin(acrsin(\frac{1}{2}x))acrcos(\frac{1}{2}x)*\frac{1}{2} - sqrt(3) - x*0*\frac{1}{2}*3^{\frac{1}{2}}\\=&\frac{acrcos(\frac{1}{2}x)}{2} - cos(acrsin(\frac{1}{2}x)) + \frac{acrxsin(acrsin(\frac{1}{2}x))cos(\frac{1}{2}x)}{2} - sqrt(3)\\ \end{split}\end{equation} \]

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